# A Verifications of running charge / running mass

#### metroplex021

Summary
Looking for citations of experimental confirmations of electronic running charge, and also running mass (if these exist).
Hi everyone,
I understand that the phenomenon of running charge predicted by QFT has been experimentally verified: the physical charge on an electron really does vary with the energy at which it is measured. I have two questions:
(1) Does anyone know what the canonical experiments confirming this are?
(2) Has there been a similar experimental confirmation of its 'running mass' (since formally mass behaves just like a coupling here)?
Any input most appreciated. Thanks!

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#### Orodruin

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Mass is not the same as coupling. The physical mass is independent of the renormalisation scale. It refers to the pole of the propagator.

• vanhees71 and metroplex021

#### Reggid

You can for example measure the running mass of the bottom quark from Z-boson decays and compare it to the running mass measured at lower scales:

https://arxiv.org/abs/hep-ph/9905495v2 states a value of
$m_b(m_Z)=2.56\pm 0.72(\rm{stat.})^{+0.28}_{-0.38}(\rm{syst.})^{+0.49}_{-1.48}(\rm{theor.})$ GeV,
the PDG quotes
$m_b(m_b)=4.18^{+0.03}_{-0.02}$ GeV.

• vanhees71 and metroplex021

#### metroplex021

Mass is not the same as coupling. The physical mass is independent of the renormalisation scale. It refers to the pole of the propagator.
Thank you Orodruin. I thought the pole mass was just the mass of the *free* particle in its own frame -- which is why, given confinement, the pole mass isn't well-defined for quarks. And I thought that the 'running' mass of the particle was its effective mass when undergoing interactions at scale E. Is that not right?

#### metroplex021

You can for example measure the running mass of the bottom quark from Z-boson decays and compare it to the running mass measured at lower scales:

https://arxiv.org/abs/hep-ph/9905495v2 states a value of
$m_b(m_Z)=2.56\pm 0.72(\rm{stat.})^{+0.28}_{-0.38}(\rm{syst.})^{+0.49}_{-1.48}(\rm{theor.})$ GeV,
the PDG quotes
$m_b(m_b)=4.18^{+0.03}_{-0.02}$ GeV.
Thank you Reggid. Is this consistent with what Orodruin writes above - ie what we're measuring when we measure this 'running mass' is something different from the mass of bottom quark itself?

#### Reggid

Due to confinement the pole mass of a quark is not more a physical mass than any other mass scheme. The pole mass is only a strictly perturbative concept, since the full propagator of a quark does not have a pole due to non-perturbative effects.

This leads to an ambiguity in the definition of the pole mass of order $\mathcal{O}(\Lambda_{\rm{QCD}})$, which is the reason why you will usually not see pole mass values for quarks very often. The only exception is the top quark, but also here this ambiguity might start to play a role when LHC takes more data and gains higher precision on top mass measurements, definitely with possible future lepton-colliders.

• vanhees71

"Verifications of running charge / running mass"

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